CBS did not immediately respond to requests for comment on the situation from CNBC.
Talarico on Tuesday posted a link to his interview with Colbert, which was available online.
In a statement provided to CNBC by his Senate campaign, Talarico said, "I think [President] Donald Trump is worried we're about to flip Texas. This is the party that ran against cancel culture."
"Now they're trying to control what we watch, what we say, and what we read," Talarico said.
"This is the most dangerous kind of cancel culture, the kind that comes from the top. A threat to one of our First Amendment rights is a threat to all of our First Amendment rights."
Talarico is in a close Democratic primary for a U.S. Senate seat against Rep. Jasmine Crockett, D-Texas, in which early voting began Tuesday. The winner will face off against the winner of the Republican primary between Sen. John Cornyn and Texas Attorney General Ken Paxton. Democrats last won a statewide race in Texas in 1994.
The FCC didn't immediately respond to a request for comment about whether CBS would have run afoul of agency guidance by airing Talarico's interview.
FCC Commissioner Anna Gomez, in a statement, called CBS's decision "yet another troubling example of corporate capitulation in the face of this Administration's broader campaign to censor and control speech."
"The FCC has no lawful authority to pressure broadcasters for political purposes or to create a climate that chills free expression," Gomez said.
"CBS is fully protected under the First Amendment to determine what interviews it airs, which makes its decision to yield to political pressure all the more disappointing," Gomez said. "It is no secret that Paramount, CBS's parent company, has regulatory matters before the government, but corporate interests cannot justify retreating from airing newsworthy content. The FCC is powerless to impose restrictions on protected speech, and any attempt to intimidate broadcasters into self-censorship undermines both press freedom and public trust."
"I once again urge broadcasters and their parent companies to stand firm against these unlawful pressures and continue exercising their constitutional right to speak freely and without government interference."
Paramount Skydance has launched a hostile tender bid for Warner Bros. Discovery, a deal that would require regulatory approval from the federal government if WBD shareholders accept the offer.
CBS in July said Colbert's show would be cancelled in May.
That announcement came shortly after Colbert blasted the network for giving what he called a "big fat bribe" to Trump. Paramount Skydance, earlier agreed to pay $16 million for Trump's future presidential library to settle a lawsuit over the editing of a "60 Minutes" interview with then-Vice President Kamala Harris.
A week after CBS said it was cancelling Colbert's show, the FCC approved the $8 billion merger between Paramount and Skydance Media.
Colbert, in September, spoke up for ABC late-night talk show host Jimmy Kimmel when ABC pulled Kimmel off the air following remarks by FCC Chair Brendan Carr that the network's broadcast license was at risk because of comments Kimmel made about the alleged killer of conservative activist Charlie Kirk.
Kimmel's show returned to the air about a week later.